The role of accelerometer-derived sleep traits on glycated haemoglobin and glucose levels: a Mendelian randomization study

Self-reported shorter/longer sleep duration, insomnia, and evening preference are associated with hyperglycaemia in observational analyses, with similar observations in small studies using accelerometer-derived sleep traits. Mendelian randomization (MR) studies support an effect of self-reported insomnia, but not others, on glycated haemoglobin (HbA1c). To explore potential effects, we used MR methods to assess effects of accelerometer-derived sleep traits (duration, mid-point least active 5-h, mid-point most active 10-h, sleep fragmentation, and efficiency) on HbA1c/glucose in European adults from the UK Biobank (UKB) (n = 73,797) and the MAGIC consortium (n = 146,806). Cross-trait linkage disequilibrium score regression was applied to determine genetic correlations across accelerometer-derived, self-reported sleep traits, and HbA1c/glucose. We found no causal effect of any accelerometer-derived sleep trait on HbA1c or glucose. Similar MR results for self-reported sleep traits in the UKB sub-sample with accelerometer-derived measures suggested our results were not explained by selection bias. Phenotypic and genetic correlation analyses suggested complex relationships between self-reported and accelerometer-derived traits indicating that they may reflect different types of exposure. These findings suggested accelerometer-derived sleep traits do not affect HbA1c. Accelerometer-derived measures of sleep duration and quality might not simply be ‘objective’ measures of self-reported sleep duration and insomnia, but rather captured different sleep characteristics.

www.nature.com/scientificreports/Prospective cohort studies have identified associations of self-reported short and long sleep duration, insomnia (difficulty initiating or maintaining sleep), and chronotype (evening preference) with higher risks of type 2 diabetes (T2D) 1-3 , hyperglycaemia and insulin resistance 4 .A small number of studies have assessed sleep characteristics using accelerometry devices, assuming these reflect similar sleep characteristics measured with greater precision and less measurement error than self-reported traits.Several observational studies showed that accelerometerderived shorter sleep duration and lower sleep efficiency (an assumed indicator of insomnia 5 ) were associated with higher glycated haemoglobin (HbA1c) levels in people with diabetes 6,7 .In a general population, higher sleep fragmentation 8 (another indicator of insomnia 9 ), but not shorter accelerometer-derived sleep duration 10 , was associated with higher HbA1c and glucose levels.However, these were relatively small studies that included ~ 170 to ~ 2107 participants, which are also open to residual confounding and/or reverse causation.A meta-analysis of randomized controlled trials (RCTs) showed that sleep restriction had detrimental effects on insulin sensitivity 11 , as well as hyperglycaemia supported by experimental data in healthy volunteers 12 .Several mechanisms have been proposed to link the effects of sleep restriction on glycaemia levels including physiological stress, activation of the sympathetic nervous system and/or circadian disruption, all of which might act on glucose levels via insulin signalling mechanisms 11 .However, the relevance of experimental sleep restriction protocols to the sleep patterns experienced in the general population is unclear.
Mendelian randomization (MR) is increasingly used to explore lifelong effects because it is less prone to confounding by social, environmental, and behavioural factors 13 .Previous MR studies showed that self-reported frequent insomnia symptoms causes higher HbA1c [14][15][16] , whilst no evidence has been provided for effects of selfreported sleep duration or chronotype on T2D and/or glycaemic traits 14,17 .Recent MR studies suggested causal effects of accelerometer-derived shorter sleep duration and lower efficiency on higher waist-hip ratio but not T2D or other hyperglycaemic outcomes in the UK Biobank (UKB) 17,18 .
Our aim was to explore potential effects of accelerometer-derived sleep traits (duration, mid-point least active 5-h (L5 timing), mid-point most active 10-h (M10 timing), sleep fragmentation, and sleep efficiency) on HbA1c.We undertook one-sample MR (1SMR) analyses using the UKB sub-sample (n = 73,797) with valid accelerometer measures.Since those with accelerometer data were not a random sub-sample of UKB, we explored possible selection bias by re-running, in this sub-sample, all of our previous MR analyses of self-reported sleep traits (duration, chronotype, insomnia) with HbA1c that had been conducted in the larger UKB sample (n = 336,999) 14 .Additionally, we conducted two-sample MR (2SMR) analyses using summary outcome data from UKB and the Meta-Analyses of Glucose and Insulin-related traits Consortium (MAGIC) 19 .Lastly, to help understand any differences we observed between self-reported and accelerometer-derived MR effects for assumed equivalent traits, we calculated the phenotypic correlations, as well as used cross-trait linkage disequilibrium score regression (LDSC) 20 to determine genetic correlations across all accelerometer-derived and self-reported sleep traits.To explore the possibility of reverse causality, we applied bidirectional 1SMR in to assess the roles of glycaemic traits on sleep traits in the UKB participants with valid accelerometer and genetic data (n = 73,797).We repeated all analyses with glucose as a secondary outcome.

Baseline characteristics
Figure 1 showed the flow of participants in the UKB sub-sample where the 1SMR analyses were conducted.Participants in the accelerometer-derived sub-sample were more likely to have never smoked, have completed advanced-level education, have a lower prevalence of diabetes and a lower mean BMI than those in either comparison group (i.e., (1) UKB European participants without accelerometer-derived data and (2) all UKB European participants with available genetic data).Other characteristics, including self-reported sleep traits were similar across the three groups (Table 1).

MR results
In 1SMR analysis (genetic instrument-exposure and genetic instrument-outcome associations were estimated in the UKB sub-sample with accelerometer-derived sleep data (n ~ 73,000)), we generated unweighted allele scores for both accelerometer-derived and self-reported sleep traits as the total number of sleep trait increasing alleles present for each participant, based on SNPs identified in the relevant GWAS.Supplementary Table S1 provides details of each SNP.The variance (R 2 ) explained by the allele scores varied from 0.04% for M10 timing (F-statistic: 30) to 0.74% for sleep fragmentation (F-statistic: 553) among accelerometer-derived traits, and from 0.54% for sleep duration (F-statistic: 401) to 2.12% for chronotype (F-statistic: 1593) among self-reported traits (Supplementary Table S2).The distributions of allele scores of all the sleep traits, except for M10 timing (only 1 SNPs was available and hence we were only able to use the per-allele association (0, 1, 2) for M10 timing), were normal.The mean and standard deviation (SD) of the allele scores were show in Supplementary Table S2.
We conducted two sets of 2SMR analyses with the SNP-exposure associations for both of these analyses obtained from the relevant GWAS 16,18,21,22 as used for 1SMR, and the SNP-HbA1c associations were obtained from two different sources: (1) SNP-HbA1c associations were estimated in UKB participants who did not participate in the accelerometer-derived GWAS 18 study (referred to as 2SMR-UKB, n = ~ 292,000); (2) SNP-HbA1c associations were extracted from the MAGIC consortium GWAS 19 (referred to as 2SMR-MAGIC, n = ~ 147,000).In the two sets of 2SMR (i.e., 2SMR-UKB and 2SMR-MAGIC), the R 2 explained and the F-statistics for sleep traits were similar, ranging from 0.04% for M10 timing (mean F-statistic: 37) to 0.91% for sleep fragmentation (mean F-statistic: 37) among accelerometer-derived traits, and from 0.68% for sleep duration (mean F-statistic: 40) to 2.78% for chronotype (mean F-statistic: 57) among self-reported traits (Supplementary Table S2).Post hoc calculations indicated that the minimum effects (in SD of outcome per SD exposure units; i.e. the equivalent of a Pearson's correlation coefficient) we demonstrated that we had power to detect small effects at 80% power at 0.05 significance in our fixed samples sizes using 2SMR.These minimum effects ranged from 0.04 to 0.35, with all but one being equal or less than 0.15; full results are shown in Supplementary Table S2 and further information on calculations in Supplementary Information.
1SMR suggested longer mean accelerometer-derived sleep duration reduced mean HbA1c levels (− 0.11, 95% CI − 0.22 to 0.01 SD per hour longer over 24-h).However, the association was attenuated to the null in sensitivity analyses accounting for any possible horizontal pleiotropy (i.e., collider-correlated estimates 23 , see "Methods") in 1SMR; 2SMR main and sensitivity results provided no robust evidence of an effect of accelerometer-derived sleep duration on HbA1c (Fig. 2 and Supplementary Table S3).For all other accelerometer-derived sleep traits, MR estimates did not support any evidence of causal effects on HbA1c (Fig. 2 and Supplementary Table S3).Results (1SMR and 2SMR-UKB) were broadly consistent when participants with diabetes were excluded (Supplementary Tables S3 and S4).There was no evidence suggesting any effect of accelerometer-derived sleep traits on glucose (Fig. 3 and Supplementary Table S4).In 1SMR, the associations of self-reported traits with HbA1c/ glucose in the UKB sub-sample with accelerometer-derived data (used here) were consistent, though with wider confidence intervals, with those we previously published using the larger samples 14 (Supplementary Fig. S1).

Phenotypic and genetic correlations and MVMR
We used LDSC 20 regression to determine genetic correlations across all accelerometer-derived 18 and selfreported 16,21,22 sleep traits and HbA1c/glucose 19 using GWAS summary statistics.Strong genetic correlations were demonstrated among the three sleep timing traits (accelerometer-derived L5 timing, M10 timing, and  ) and minus those who failed the accelerometer data quality control check (n = 5049).† Townsend deprivation index was calculated using data from the preceding national census output areas, where each participant was assigned, a continuous score corresponding to the output area of their postcode location.A higher index indicates a greater level of deprivation.‡ Alcohol intake was categorized and adjusted as "Daily", "One or four times a week", "Once or twice a week", "One to three times a month", "Occasionally", "Never"; vigorous physical activity was categorized as days from 0 to 7 per week.(Details in Supplementary Information).§ Sleep apnea (ICD-10) was diagnosed from the Hospital Episode Statistics (HES) data.www.nature.com/scientificreports/self-reported chronotype; all R LDSC > 0.8).There was modest genetic correlation between accelerometer-derived and self-reported sleep duration (R LDSC = 0.43) and relatively strong genetic correlation between accelerometerderived sleep duration and sleep efficiency (R LDSC = 0.72).Genetic correlations of self-reported insomnia with both accelerometer-derived efficiency and fragmentation were weak (both R LDSC < 0.18), with modest correlation between accelerometer-derived sleep fragmentation and sleep efficiency (R LDSC = − 0.52).There were weak negative genetic correlations of self-reported sleep duration with HbA1c (R LDSC = − 0.07) and glucose (R LDSC = − 0.07), and weak positive genetic correlation of insomnia with HbA1c and glucose (R LDSC ≤ 0.1) (Fig. 4 and Supplementary Table S5).Most of the phenotypic correlations agreed with the LDSC genetic correlations though the strength was weaker (Supplementary Fig. S2 and Supplementary Table S5).
We repeated MR analyses with mutual adjustment using multivariable Mendelian randomization (MVMR) 24 to account for strong correlations between accelerometer-derived sleep traits (i.e., between L5 and M10, and between accelerometer-derived sleep duration and efficiency).These results did not differ from the main results, suggesting no independent causal effect of L5, M10, accelerometer-derived sleep duration or efficiency on HbA1c or glucose (Supplementary Table S6).

Bidirectional MR
We assessed the effects of HbA1c and non-fasting glucose on both the accelerometer-derived and self-reported sleep traits in UKB participants with valid accelerometer and genetic data.The two-stage least square estimates suggested no effect of HbA1c on no sleep traits except for L5 timing (− 0.36, − 0.66 to − 0.07 h per log mmol/ mol).There was some evidence of an effect of higher non-fasting glucose levels on reducing the number of sleep episodes (− 2.3, − 4.0 to − 0.5 time per log mmol/l) and on higher sleep efficiency (3.9, 0.4-7.4% per log mmol/l) (Supplementary Table S7).

Discussion
In this, to the best of our knowledge, first MR study to explore causal effects of accelerometer-derived sleep traits on glycaemia.We found no robust evidence that any assessed sleep traits causally affected HbA1c or glucose, including across a suite of sensitivity analyses and in MVMR adjusting for between-trait correlations.The null effects of accelerometer-derived sleep traits were unlikely to be explained by selection bias.We showed strong positive genetic correlations between accelerometer-derived L5 and M10 timing, and self-reported chronotype, suggesting that accelerometer-derived and self-reported measures for sleep timing were capturing the same trait.By contrast, positive correlations between accelerometer-derived and self-reported sleep duration were modest.Those between self-reported insomnia and two accelerometer-derived measures (i.e., low sleep efficiency and high sleep fragmentation) that might be expected to relate to insomnia were weak.Lastly, we found no effect of www.nature.com/scientificreports/sleep fragmentation or efficiency on HbA1c, though effects of insomnia were identified previously 14 .Accelerometer-derived measures of sleep duration and sleep quality might not simply be 'objective' measures of selfreported sleep duration and insomnia, but rather they might capture different underlying sleep characteristics.Our MR findings do not support the observational associations of accelerometer-derived sleep measures (e.g., shorter sleep duration 6 , lower sleep efficiency 7 , higher sleep fragmentation 8 ) with higher glycaemia levels.These observational relationships might be explained by residual confounding, as well as reverse causality as most previous observational studies were cross-sectional.For example, undiagnosed hyperglycaemia might cause nocturia 25 and/or neuropathic pain 26 , which could result in reduced sleep duration and poor sleep quality.Our bidirectional 1SMR estimates only indicated potential effects of HbA1c on L5 timing as well as glucose on sleep fragmentation and efficiency.These results will need to be independently replicated before assuming they are causal.Our MR findings also do not support data from randomised controlled trials which have shown that sleep restriction reduces insulin sensitivity, at least in short-term studies 11 .
Sleep characteristics might be captured differently through assessment of self-reported and accelerometerderived traits.For instance, the self-reported sleep duration question includes naps but this is not the case for accelerometer-derived sleep duration.The phenotypic and genetic correlations (R = 0.18 and R LDSC = 0.43) also indicated a modest-to-weak correlation, which was consistent with previous findings 18,27 .The null MR estimates of accelerometer-derived sleep fragmentation and efficiency (assumed measures of insomnia 5,9 ) with HbA1c contrasted with previous MR results suggesting that self-reported frequent insomnia symptoms results in higher HbA1c levels [14][15][16] .Several factors could explain these differences.Self-reported insomnia is by definition experienced, and that experience, rather than the sleep disturbance, might cause or be a proxy for adverse mental or physical health, such as depression/anxiety 28 , endocrine disorders 29 , and/or appetite changes 30 , that influence HbA1c.Besides, sleep can be disturbed in ways not detectable by actigraphy or even polysomnography.Therefore, accelerometer-derived sleep fragmentation and efficiency might only reflect insomnia status in terms of sleep changes, but not mental or physical changes.The low phenotypic and genetic correlations of accelerometer-derived sleep fragmentation (R = 0.03 and R LDSC = 0.09) and efficiency (R = − 0.04 and R LDSC = − 0.18) with self-reported insomnia supports this idea to some extent.It is also possible that genetic contributions to selfreported and accelerometer-derived measures of insomnia/sleep quality differed, though heritability estimates using UKB data suggested these were similar (17% for self-reported insomnia 31 and 22% for accelerometerderived fragmentation 18 ).Further studies exploring what might contribute to weak/modest correlations between self-reported and accelerometer-derived measures of sleep duration and quality/insomnia are important, though noting that actigraphy data provides limited data about sleep physiology in terms of macro or microstructure 32 .Lastly, there are potential differences between neurological sleep and sleep defined by accelerometry devices and self-reported questionnaires.Systematic comparisons in large studies with polysomnography as well as self-report and accelerometer data would be needed.Currently, we are not aware of any such studies.
A key strength of this study is its novelty in using MR to explore potential causal effects of accelerometerderived sleep traits on HbA1c and glucose.We conducted 1SMR, 2SMR, and a range of sensitivity analyses to explore genetic instrument validity.The consistency of findings across these methods, and across samples, increases confidence in our conclusion that accelerometer-derived sleep traits do not have causal effects on HbA1c or glucose.
We acknowledge the following potential limitations.Whilst we have used the largest available cohort with accelerometer-derived sleep data and genomic data, and, to our knowledge, this is the first MR study of these exposures with HbA1c and glucose, we acknowledge that the statistical power may have been limited for some results.Although our post hoc calculations demonstrate that, not for all but one of our 2SMR analyses, we have power to detect small effects of equal or less than 0.15 SD/SD (i.e. the equivalent of a Pearson correlation coefficient ≤ 0.15), the value of such post hoc calculations is contested [33][34][35] .In studies like ours, the observed point estimates and their confidence intervals are more valuable ways to interpret results and statistical power 34 .For example, our 2SMR suggested that one hour longer mean accelerometer-derived sleep duration would change mean HbA1c levels by − 0.09 (95% CI − 0.2 to 0.03) (SD unit, 1SD = 0.41%) (Fig. 2).Since the SD for HbA1c was 5.5 mmol/mol (Table 1), our data indicated that lengthening sleep duration by 1 h over 24 h is likely to change HbA1c values by somewhere between − 1.1 (− 0.2*5.5)and + 0.2 (0.03*5.5) mmol/mol.In the setting of diabetes, a 3 mmol/mol decrease in HbA1c is generally considered to be 'clinically important for reducing the risk of developing diabetes-related complications 36 .Thus, it can be seen that the 95% CI for our causal effect estimate excludes a 'clinically significant' effect.In summary we have power in 2SMR to detect small effects and our 95% confidence intervals suggest there are unlikely to be clinically important effects.
Our results could be influenced by selection bias 37 , due to the low recruitment into UKB (5.5% participation 38 ), as well as the non-random selection of UKB participants into the accelerometer-derived sub-sample resulting in a healthier accelerometer-derived sub-sample of UKB.Whilst the low participation into UKB could result in selection bias 39 , similar observational and MR associations with a range of outcomes have been obtained in meta-analyses with/without UKB participants being included, where other cohorts had higher response rates (i.e.≥ 70%) 40,41 .Besides, in this study, when we compared 1SMR estimates of self-reported sleep traits on HbA1c/glucose in the accelerometer-derived sub-sample to the same results in a much larger UKB sample that we previously published 14 , we found similar results, suggesting minimal bias due to selection.Results did not differ in sensitivity analyses that excluded participants with diabetes, suggesting our results are not influenced by having diabetes or treatment with hypoglycaemics.We assumed the genetic instrument reflects lifetime exposure.Although the accelerometer-derived data was obtained sometime after the measure of HbA1c, there was unlikely a concern of reverse causality in an MR design.If not the case (i.e., there was reverse causality), we would expect the results to be biased away from the null, which is contrary to our findings.Our sensitivity estimates (bidirectional 1SMR) did not suggest an effect of HbA1c on any of the sleep traits except for L5 timing and, as noted above, the effects of non-fasting glucose on accelerometer measured sleep efficiency and sleep fragmentation reflecting insomnia.www.nature.com/scientificreports/These could be chance findings.Because, no consistent effect of HbA1c on other sleep timing traits was found.
Besides, collider bias is a potential concern given the glucose robust SNPs were from a GWAS in which BMI was adjusted (i.e., SNP-glucose associations could be biased following BMI adjustment), these results require replication 42 .We used genetic variants that passed a p-value threshold of p < 5 × 10 −8 in UKB, but with limited evidence of replication in an independent cohort 18 .Without further replication in larger studies, it was possible that some of the 44 SNPs were false positives and/or had inflated associations with sleep traits, which could result in both our 1SMR and 2SMR results being biased towards the null 43 .However, a recent study has suggested the use of SNPs from GWAS that have not been independently replicated may not result in notable bias 44 .Participants were predominantly of European ancestry, meaning our findings may not generalise to other ancestries.Lastly, our study assumed linear associations between accelerometer-derived sleep traits and HbA1c/glucose.If there was a symmetrical U-shaped association, this linear assumption would bias results toward the null.

Conclusions
We found little evidence to support causal effects of any accelerometer-derived sleep trait on HbA1c or glucose levels across a wide range of MR methods.We cannot rule out non-linear (e.g., U-shaped) effects and acknowledge the need for further GWAS and MR studies of accelerometer-derived traits in larger diverse populations.

Methods
This study is reported as per the Strengthening the Reporting of Observational Studies in Epidemiology (STROBE) guideline 45 , specific for Mendelian randomisation Information).

The UK Biobank
Between 2006 and 2010, the UKB recruited 503,317 adults (aged 40-69 years) out of 9.2 million invited eligible adults (5.5% response) 38 .Information on socio-demographic characteristics and lifestyle including self-reported sleep traits were obtained using a touchscreen questionnaire at the baseline assessment.Venous blood samples were collected and processed at baseline.Between February 2013 and December 2015, participants, except for those from the North West region (who had been invited to participate in a separate sub-study), were approached by email to participate in the accelerometer study.The valid email addresses were chosen randomly.From June 2013, those who agreed to participate were sent a triaxial accelerometer device (Axivity AX3) device in order of acceptance.It was worn continuously for up to seven days in a sub-sample of participants (n = 103,711) an average of five years after the baseline assessment (range 2.8-8.7 years) 18,46 .Figure 1 shows the flowchart of participants from all recruited to those included in our study.After applying pre-specified exclusion criteria, we included 73,797 European participants 47 with accelerometer-derived sleep data in the analyses.Full details are presented in Supplementary Information.

Accelerometer-derived sleep traits
(1) Accelerometer-derived nocturnal sleep duration was defined as the summed duration of all nocturnal sleep episodes within the sleep period time windows (SPT-windows).Sleep episodes were defined as any period of at least 5 min with no change larger than 5° associated with the z-axis of the accelerometer 48 .The algorithm in GGIR (R package) combined all sleep episodes that were not separated by more than 30 min and then called that the SPT-window (of which there can only be one per day).Any sleep episodes outside of this window were classified as naps and so did not count towards the nocturnal sleep duration total.The total duration of all SPT-windows over the activity-monitor wear time was averaged and divided by the number of days (24 h) to give mean sleep duration per total day.Individuals with an average sleep duration < 3 (n = 147) or > 12 h (n = 3) were set to missing in this study.(2) Midpoint least-active 5-h (L5) timing was a measure of the midpoint of the least-active (i.e., with minimum average acceleration) 5 h of each day.The 5-h periods were defined on a rolling basis (e.g., 1:00-6:00, 2:00-7:00 and so on).For example, if the midpoint of the least-active 5-h was 24:00 (0:00) (i.e., a rolling 5-h was from 21:30 to 2:30) then L5 = 24 (i.e., 24 + 0); if the midpoint of least-active 5-h was 3:30 then L5 = 27.5 (i.e., 24 + 3.5); and if the midpoint of the least-active 5 h was 20:30 then L5 = 20.5 (i.e., 24 − 3.5).Thus, a higher L5 score indicated someone was least active in the morning and more likely to have an evening chronotype.
(3) Midpoint most-active 10-h (M10) timing was a measure of the midpoint of the most active (i.e., with maximum average acceleration) 10-h time of day based on a 24-h clock.It was calculated in a similar way to L5 (see above) except with rolling periods of 10 h.A higher M10 score indicated someone who was most active in the evening and hence more likely to have an evening chronotype (4) Nocturnal sleep episode (defined above) was a measure of sleep fragmentation.Individuals with an average number of sleep episodes ≤ 5 (n = 84) or ≥ 30 (n = 52) times were set to missing in this study.We referred to a high number of sleep episodes as 'sleep fragmentation' throughout this paper.(5) Mean sleep efficiency was calculated as the nocturnal sleep duration (defined above) divided by the time elapsed between the start of the first inactivity bout and the end of the last inactivity bout (which equals the SPT-window duration) across all valid nights.This was an approximate measure of the proportion of time spent asleep while in bed.

Sensitivity and additional analyses
Accounting for the impact of diabetes.To account for the potential impact of either diabetes or the diabetic treatment on glycaemic levels, we repeated the analyses with UKB participants (1SMR and 2SMR-UKB) excluding those with diabetes defined by the Eastwood algorithm (probable/possible type 1 diabetes and type 2 diabetes, based on self-reported medical history and medication) 55 and/or additionally those with a baseline HbA1c ≥ 48 mmol/mol (≥ 6.5%, the threshold for diagnosing diabetes).
Assessing MR assumptions and evaluating bias.MR analysis requires three key assumptions to be satisfied in order to obtain valid causal estimates 56 .First, the genetic instrument should be statistically robustly associated with the exposure.We investigated this using first-stage F-statistic and R 2 .In addition, we undertook a post-hoc calculation of the minimum effects (in SD of exposure per SD outcome units) that we could detect at 80% power and 0.05 significance level in our fixed sample sizes for all of the 2SMR analyses.Further details are presented in the Supplementary Information.An F-statistic < 10 is has been proposed as indicating the potential weak instrument bias 57 .However, this threshold is arbitrary and in general the higher the R 2 and F-statistic the less likelihood of weak instrument bias.Second, there should be no confounding between the genetic instrument and the outcome.This can occur as a result of population stratification.We attempted to minimise this by restricting analyses to European ancestry and adjusted for genetic principal components and assessment centre 53 .Third, the genetic instrument should influence the outcome exclusively through its effect on the exposure.This would be violated by unbalanced horizontal pleiotropy (i.e., an independent pathway between the instrument genetic variant and outcome other than through the exposure).We have undertaken the following sensitivity analyses to explore potential bias due to horizontal pleiotropy.
In 1SMR, we explored between SNP heterogeneity, potentially due to horizontal pleiotropy, via the Sargan over-identification test 58 .Additionally, we applied the Collider-Correction 23 method to implement three further pleiotropy sensitivity analyses commonly used in 2SMR (i.e., IVW, MR-Egger, and least absolute deviation regression (LADreg) being similar to the weighted median (WM) approach).Collider-Correction was needed in 1SMR to account jointly for pleiotropy and weak instruments bias 57 (Supplementary Information).We subsequently referred to this as 1SMR with Collider-Correction as 1SMR-CC (i.e., 1SMR-CC-IVW, 1SMR-CC-MR-Egger, 1SMR-CC-LADreg).In 2SMR, we explored unbalanced horizontal pleiotropy by comparing the results of the IVW regression with standard pleiotropy-robust MR methods: WM and MR-Egger, referred to as 2SMR-UKB/ MAGIC WM and 2SMR-UKB/MAGIC MR-Egger.To account for weak instrument bias in the 2SMR MR-Egger estimates, we used simulation extrapolation SiMEX 59 .We referred it as 2SMR-UKB/MAGIC MR-Egger_SiMEX.
Exploring selection bias.We compared distributions of HbA1c, glucose, diabetes prevalence, BMI, and a range of socioeconomic and behavioral characteristics between those included in the sub-sample of UKB with accelerometer-derived data (n = 73,797) and those not in this sample (n = 306,317), as well as the whole available UKB sample (n = 385,163), because the accelerometer-derived sub-sample were recruited non-randomly.In addition, we compared the 1SMR estimates of self-reported sleep traits (sleep duration, chronotype, insomnia symptoms) on HbA1c/glucose in this study (n = 73,797) with those 1SMR estimates, previously published in nearly all UKB participants 14 (n = 336,999, White British ancestry).Similar estimates would suggest limited risk of selection bias.
Phenotypic and genetic correlation between sleep traits.We used adjusted Pearson correlations to assess the correlations across the sleep traits, as well as with HbA1c and glucose for consistency, though some of the sleep traits were categorical (e.g., SR sleep duration, chronotype, insomnia).Pearson correlation can be interpreted as the regression coefficient one would obtain regressing the standardised (SD units) of two variables on each other.We adjusted for baseline age, sex, genotyping chip, assessment centre and 40 genetic principal components.
We used linkage disequilibrium score regression (LDSC) 20 (Supplementary Information), as an additional analysis, to aid the interpretation of the MR using accelerometer-derived results and interpret any differences that might be observed between our accelerometer-derived data generated and our previously reported MR effects of self-reported sleep traits on HbA1c/glucose 14 .We assessed genetic correlations between all accelerometer-derived and self-reported sleep traits.For completeness, we also explored genetic correlations of each accelerometerderived and self-reported traits with HbA1c and glucose.The full summary statistics of all sleep traits were obtained from the Sleep Disorder Knowledge Portal https:// sleep.hugea mp.org/.Those for HbA1c and glucose were from the MAGIC consortium 19 .
Whenever we observed strong genetic correlation between any two accelerometer-derived sleep traits (i.e., ≥ 0.7) regarding robustness of the univariable MR estimates, we undertook multivariable Mendelian randomization (MVMR) 24 to explore whether we could determine individual accelerometer-derived sleep trait direct effect (Supplementary Information).
Bidirectional MR.To explore whether variation in HbA1c and glucose might influence variation in sleep traits we selected genome-wide significant independent SNPs predicting HbA1c (n = 74) and BMI-adjusted fasting glucose (n = 66) from a large multi-ancestry GWAS (European specific data was applied) 19 (Supplementary

Figure 1 .
Figure 1.Flowchart of the participants included in the main analyses in the UK Biobank.*Quality control procedure undertaken, and the derived files produced by the MRC-IEU (University of Bristol), using the full UK Biobank genome wide SNP data (version 3, March 2018).https:// data.bris.ac.uk/ data/ datas et/ 1ovaa u5sxu np2cv 8rcy8 8688v.The number of 79,460 was obtained after accounting for overlapped samples.† Excluding participants with diabetes defined by the Eastwood algorithm (probable/possible type 1 diabetes and type 2 diabetes) and/or additionally those with a baseline HbA1c ≥ 48 mmol/mol.
accelerometer-derived data (n = 306,317) is obtained from the whole European sample with self-reported sleep trait data and genetic data (n = 385,163) minus the number with accelerometer data (n = 78,846 54VW) regression of the Wald ratio for each SNP under a multiplicative random-effects model54to obtain the causal estimates.Further details are presented in the Supplementary Information.1SMRand 2SMR analyses taking self-reported sleep traits (sleep duration, chronotype, insomnia symptoms) as the exposures were conducted for comparison.The detailed information is presented in the Supplementary Information.